116 S1E B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
limit of the analysis of those units, so here another and not altogether dissimilar 
problem is suggested to us — namely, the actual analysis of all chemical events into a 
system of simple constituent events occurring in various ways by the transferences to 
and fro among the units of matter and space of these same “ simple weights.” We are 
far indeed from this ultimate ideal goal, but may yet recognize it on the far horizon 
as the limit of our speculations. 
(8) We are thus led to regard many events of an apparently simple character as 
constituted of numerous other events, some realizable, others not, the concurrence of 
which results in those events. To some, even when demonstrated, this may appear a 
complex view. But the complexity is not real. It is in truth the simplest possible 
doctrine. We may compare the aggregates of simple events of which compound events 
are constituted to the aggregate of the repeated blows of the hammer, by which (each 
falling with a certain force and in a certain requisite direction) two or more pieces of 
iron are welded together and shaped to a determinate form. What is here effected is 
to specify the kind of blows which are required and the number of blows of each kind. 
Now it may be asked, since every chemical event is here referred to one set of causes, 
and regarded as occurring by the transferences of the “ simple weights ” «, , 
How are we to interpret such expressions as [x— a), ( xy—ab ), when they occur among 
the factors of chemical equations X Such expressions apparently involve a change in our 
point of view; for [x— a) is not the symbol of the “ transference ” of x, but of the sub- 
stitution of one “ simple weight,” a , for another, x , and [xy — ab) is not the symbol of 
any substitution of one simple weight for another, but is the symbol of the substitution 
of a compound weight ah for a compound weight xy. To this it may be replied that 
we are here considering results; that the expression [x— a) means the occurrence of a 
phenomenon of which the result is the substitution of a for x. But it does not inform 
us of any particular way in which this result is attained. And, in fact, this result may 
with equal justice be considered as the aggregate of the two transferences [x— 1) — (a— 1) 
as a single substitution. Such an expression, therefore, as [x — a)[y — b) is always to be 
regarded as an abbreviated form of expression for the aggregate 
[x-l)[y-l)-[x-l)[b-l)-[a-l)[y-l)+[a~ 1 )[b -1). 
Similarly, developing the expression [xy—ab), we have 
xy-ab=[x-l)+{y^l)+[x-l){y-l)-{a-l)-[b-l)-{a-l){b-l), 
so that the event symbolized (for example) as [xy— ab)(z— 1) is to be regarded as an 
abbreviated expression for the aggregate of events, 
— («—!)(*— 1)C«—1). 
It is my intention to lay before the Society, in a further communication, a set of 
examples illustrative of the application of the principles of this Calculus to the discus- 
sion of special chemical events. 
